Material Fallacies 3

Robert Harris
Version Date: June 6, 2000

Miscellaneous Fallacies of Reasoning

Compound Questions. Also called "poisoning the well," this fallacy
involves a question which at the same time presents a conclusion or consists
of a conclusion in the guise of a question. The fallacy is committed by
combining two or more questions which cannot be answered together (hence
the name "compound questions"), or more often, by asking a question implying
that a previous question has already been asked and answered in a particular
way. The compound question thus prevents or avoids any opposing arguments
and incriminates the answerer regardless of the response he gives because
any answer would admit the preliminary conclusions built into the question.
The classic, ancient example is, "Have you stopped beating your wife?"
If you say, "no," you admit that you beat her. But if you say, "yes," you
also admit that you used to beat her. Note the assumptions behind these
questions:

How often do you cheat on tests this year?

How do you account for your incompetence?

Why did you cause the Smiths' divorce?

Why do you want war?

Are you trying to impose your outdated standards on me?

Do you expect me to believe that lie?

Where did you hide the murder weapon?

Who made God?

Have you always been such a fanatic?

Why do you always commit logical fallacies when you talk?

Why won't you be convinced by obvious truth?

In another form of this fallacy, several questions which may each have
a different answer are combined into one question for which a single response
is demanded.

Mr. Glass, did you or did you not visit the bank that morning--as our witnesses
have established--and then rob it later that afternoon? Just answer yes
or no.

Are you planning to quit your job and thereby doom yourself to failure
and despair?

The response to a compound question, of course, is to refuse to answer
it as stated, identifying it as a compound question, and then breaking
it down into its various components. Questions which imply previous conclusions
should be responded to by objecting to the conclusions: "Have you stopped
beating your wife?" "I do not now beat nor ever have beaten my wife."

Note that if a previous question has indeed been asked and answered
or if some circumstance establishes the answer to a previous question,
a question that implies that previous answer is not fallacious. If someone
takes a few shots at you, you are not being illogical to ask, "Why are
you trying to shoot me?" If Johnny is always late coming home, his parents
are not being illogical to ask, "Why are you always late coming home?"

Begging the Question (Petitio Principii). In its standard
form, this fallacy occurs when the initially stated point to be proved
(the thesis or assertion) is later used in the argument as an already accepted
fact, to support some new point at issue which must be established to prove
the initial point. Thus the original statement is eventually used to prove
itself true, and hence the other name for this fallacy, circular reasoning.
Thesis A is supported by point B; point B is then supported by thesis A
(now called fact A).

(Note: The name of this fallacy is often confusing. "Question" here
means "issue" rather than "a request for an answer." Thus, a question-begging
argument usually has no actual questions in it.)

Many intelligent people believe in ghosts. This is clear because several
intelligent people told me so. And I know they were intelligent because
they all believed in ghosts.

All of the best economists follow Keynes. Joseph Line told me, and he's
clearly one of the best economists because he follows Keynes.

The fossils in this stratum are 200 million years old. How did I date them?
Well they are in a stratum of that age. How do I know the stratum is that
old? Because it contains these fossils, which are found in strata of that
age.

Sometimes essentially the same assertion is changed into different words
and used directly as "evidence" to prove itself as first given:

Things are worse than before because they are not as good as they used
to be.

I think Jones is guilty. Why? Because I think he did it.

Another form of this fallacy, known as a question-begging definition, defines
a term or phrase in such a way that, when used in an assertion, it proves
the assertion true by the very way the term is defined. Any objection to
the assertion is silenced by appealing to the definition. For instance,
if an arguer says, "All properly informed people oppose mining ocean-floor
mineral nodes," anyone named to be in favor of such mining can be declared
"not properly informed" by definition. Note the way the following implied
definitions are question begging:

All high-quality lamps use Snappo switches.

Anyone who isn't a complete dunce knows that I am right.

All those entitled to judgment will agree with my position on airbags.

Books expressing that view are not reliable.

The only way to get those results is by sloppy technique.

Question-begging definitions are often the result of stipulative definitions
taken to extremes. A stipulative definition is a special, customized meaning
given to a word for the sake of exactness or better understanding. Many
words are broad or even vague, and stipulative definitions can help to
clarify an argument or presentation. For example, no logical problem arises
when a writer specifies that "the term 'current technology' shall mean
here 'manufactured within the last two years'" or "by 'hardwood cabinet'
I mean a cabinet made from boards of solid hardwood but a cabinet made
from particle board, even though the particle board is made of hardwood
chips." These are both reasonable stipulative definitions, almost certainly
not designed to rig an argument. But compare these similar definitions
and their arguments:

Well, I define current technology as "using the Elmo-Frimpson screw system,"
and since our company is the only one using that system, we are the only
one using current technology.

The test is whether the definition establishes a conclusion automatically
and unfairly or whether it is a reasonable definition and clarification
of a vague or loose term.

Condition Contrary to Fact. We all have fun speculating on what
might have been different if certain events of history or the past had
had different outcomes. Of course, we can never be sure what would have
happened. A single event is a link in an infinitely branching chain, and
to alter that event could result in an incomprehensible number of altered
events after it. Thus, all we can do is imagine and guess--probably very
inaccurately--what would have been if some circumstance had been different.
To insist otherwise--to pretend to know what would have happened--commits
the fallacy of condition contrary to fact.

If the South had won the Civil War, we would still have slavery.

If Tillotson had been appointed to the Federal Reserve Board, the inflation
rate would be twice as high.

If we had made our toasters hot pink instead of blue, we would have sold
twenty million of them instead of only six.

If I'd gone to another school, I'd be making straight A's this semester.

If Philadelphia had remained the seat of the U.S. government, the publishing
industry would be centered there instead of in New York.

In another form of this fallacy, an arguer applies the premise of a conditional
syllogism to a circumstance that does not have a necessary or automatic
cause-and-effect relationship. We can seldom be sure what will follow a
certain proposed event until the event actually occurs. We can argue for
probability in such cases, but not for necessity. Note the difference between
the premises of acceptable conditional syllogisms like these--

If the power remains off for more that 48 hours, the food will spoil.

If the system fails to transfer control to the program, the program will
not run.

--and these examples of condition contrary to fact:

If peanut price supports are eliminated, the price of peanuts will go up,
not down.

If we reduce the amount of reading required, students will learn less.

If the U.S. put a 10,000-man standing army in the Middle East, armed conflict
there would stop.

If the California Inventory Tax is repealed, business will improve dramatically,
and many new warehouses will be built in the state.

Note that any of these last statements would serve very well for the thesis
of an essay, in which supporting evidence would help to establish that
thesis. But none of the conclusions follow necessarily from the proposed
(hypothetical) conditions. As in all other areas of critical thinking,
you must use your good judgment to determine how probable each of these
claims seems to be.

Contradictory Premises. Conclusions are drawn from the interactions
of premises: where two premises contradict each other, there can be no
interaction and hence no conclusion. Similarly, if the definitions of two
terms conflict with or exclude each other, then those two terms cannot
be simultaneously ascribed to a single object or event. The classic example
of contradictory premises is the question, "What will happen if an irresistible
force meets an immovable object?" The problem here is that in a universe
where an irresistible force has been defined to exist, there cannot also
exist an immovable object, because then the force would not be irresistible.
Conversely, if there is discovered or defined such an item as an immovable
object, then by definition there can be no such thing as an irresistible
force.

This fallacy's most popular appearance is in the form of a challenging
question, because questions with contradictory premises are such brain
teasers. In each case, though, no answer can be given because the premises
cannot both be true.

Into what shape of hole would a round square fit?

If an object is all black and all white at the same time, what color is
it?

If an object is both stationary and traveling at an infinite rate of speed,
how long will it take to meet itself?

If God can do anything, can he make a stone so heavy that he cannot lift
it?

If God is all powerful, can he put himself out of existence and come back
with twice the power he had before?

The Fallacy of Self-Refutation. Any statement asserting a universal
truth or absolute application must itself be subject to and consistent
with the doctrine it advances. Sometimes, however, a statement--especially
of epistemological philosophy--logically contradicts the philosophy it
advances; that is, the expression or assertion of a "truth" is itself an
exception or contradiction to the truth so expressed or asserted. For example,
the statement, "All generalizations are false," is itself a generalization,
so that if indeed all generalizations are false, the statement itself is
false also. Thus the statement refutes itself and is therefore logically
impossible. Note that the following statements all commit the fallacy of
self-refutation because each one contradicts in itself the assertion it
presents.

To find truth we must begin without any a priori assumptions. [This
statement is an a priori assumption.]

Nothing must be admitted as true without empirical verification. [How is
this rule to be verified empirically as true? This statement must not be
admitted as true by its own requirement.]

Nothing can be known with certainty. [Then this statement cannot be known
with certainty.]

All truth is subjective opinion. [If this statement is an objective conclusion
about truth, it contradicts itself; if it is merely a subjective opinion
about truth, it bears little weight as a principle of knowledge.]

There are no absolutes. [Is this true absolutely? Is it true partly? If
this is absolutely true--true in every case--it proves itself false by
being an absolute. If it is not true in every case, there must be absolutes
which are the exceptions, and thus the statement is still false. The statement
expresses an absolute truth and so refutes itself.]

Truth does not exist. [In that case, this statement is not true. In any
other case, the statement is proved false.]

Everything should be questioned and doubted until it is proved. [Then this
assertion must be questioned and doubted until it is proved; therefore,
the truth of this assertion is in doubt.]

Everything I say is a lie. [Then what are we to make of this statement?
How reliable is it?]

False Dilemma. This fallacy is also known as false alternatives
or the either/or fallacy. We all sometimes get into the habit of viewing
life as a series of antitheses: we hear one side of an argument and want
to hear the "other" side; one party or position must be "right" and the
other must be "wrong." Actually, there may be ten or more sides to an argument,
not just two; and one party or position may be a mixture of good, bad,
and compromised ideas, just like the other. The real circumstances of life
seldom align themselves exactly with our ideals of right and wrong, good
and bad, virtue and vice; so we must be careful not to create false alternatives
forced into correspondence with these ideals (for example, "This energy
bill is either good or bad").

Further, we must resist reducing complex situations and possibilities
to only two alternatives (or three or four). Many alternative positions
are not diametrically opposed to each other, but may be merely different
mixtures of similar ingredients. Thus, to characterize two positions as
mutually exclusive can be not only reductive, but completely false. For
example, "This is a struggle between safety and liberty," or "You support
progress but we support ecology," implies in each case that the two opposed
elements cannot be reconciled or co-existent and that the hearer must choose
between them.

A false dilemma is not always created by a careless or ignorant arguer.
A few arguers purposefully establish such a one-or-the-other choice in
order to oppose their position to an obviously false and easily rejectible
position, thereby almost forcing agreement with theirs: "We must either
put my plan into operation today or face anarchy and bloodshed tomorrow."

In today's world you must make a choice between integrity and success.

This is another obvious case of capitalism versus the working man.

Are you going to marry me or are you going to live a miserable and lonely
existence?

Which are you for--property rights or human rights?

Be slightly suspicious when you read or hear expressions like, "Our choice
is clear--we must have either . . ." or "Which will you have?" They are
often followed by a false dilemma. (Do note that not every either/or usage
is fallacious: "The patient is either alive or dead" or "Either God exists
or he doesn't" are both legitimate oppositions.)

Missing Comparison. Part of the empirical method is to compare
one thing to another and then to announce how each measures up or ranks.
A conclusion might be, "This thread has a higher tensile strength than
that thread." A fallacy occurs when a comparison or ranking is announced
without naming the thing to which it is compared, because such a "comparison"
provides no real information. Note the essential meaninglessness of a statement
like, "This thread has a higher tensile strength." To what has the thread
been compared? Another thread? A hair? A blade of grass? Since it is impossible
to make any assumption about the object of comparison, the statement tells
us nothing about the thread, though it seems to make a claim of superiority.

The fallacy of missing comparison is popular because it permits an expression
of superiority without the risk of actual commitment or the need for proof.
Whatever assumptions (or self deceptions) the hearer of the argument makes
are his own problem.

Now Soapo is 23% stronger.

You get 54% fewer cavities with Crest.

Blade-O gives you a closer shave.

Use DeeTurge for a cleaner, whiter wash.

Missing Range. Similar to missing comparison, this fallacy occurs
when only one end of a range of values is given, thus misleading understanding
or expectation. By presenting one extreme or the other, or worst case or
best case estimates, the an arguer distorts reality. Suppose Tastee Tomato
plants produce anywhere from 2 to 100 pounds of fruit per plant, with most
producing about 20 pounds. What picture of their performance would you
get by the following claims?

Hey! Tastee Tomato plants produce up to 100 pounds of fruit each! Get one
today!

Aw, Tastee Tomato plants produce as little as 2 pounds of fruit each. What
good are they?

Here are some other examples of the missing range fallacy:

Come to Oval Tires. We have radial tires from $24.95.

But his plan could cost as much as $45 million.

Wrist watches as low as $2.95.

Phrases Often Used in Missing Range

up to

starting at

as much as

as little as

beginning at

as many as

as few as

from

as high as

as low as

Misleading Average. Making an assertion about an average often
reveals little and more often obscures truth, first because there are three
distinct kinds of average and second because each kind can easily distort
reality.

The three kinds of average are as follows:

1. Mean or arithmetic average, the most common kind, is obtained
by dividing the sum of all the items in a group by the number of items.
For example, in the group 3, 3, 8, 10, the mean is 6 (3 plus 3 plus 8 plus
10 equals 24, divided by 4 equals 6).

2. Median or halfway point is the number at the point in an arithmetically
arranged list where half the items are larger (or above) and half are smaller
(or below). Thus, the median in the list of 42, 54, 79, 108, 929 would
be 79, because it is at the midway point.

3. Mode average is the most frequently occurring item in a list.
The mode of 6, 6, 9, 19, 19, 72, 72, 72, 108 would be 72 because it occurs
the most often.

When an arguer does not specify the kind of average he refers to as
just "the average," a considerable amount of deceit and distortion can
be perpetrated. Suppose you see an advertisement for real estate sales
positions. It reads, "Earn up to $350,000 a year! Salesmen in our office
average $59,000 a year!" Here are the facts from which that claim
was taken:

Yes, both claims in the advertisement are quite true: you can earn up
to $350,000 a year and the mean average is indeed $59,000. But
do those claims present the situation fairly, or give you information on
which you can base an accurate estimate of your own earnings? Over 86%
of the salesmen earn $13,000 or less. Therefore, by not naming the kind
of average used here, and because each kind differs so largely, and because
an unspecified average is a misleading average, this advertisement is fallacious.
Here are some other examples:

The average American used car is 3.6 years old.

The average income these days is $24,000.

Another kind of misleading average occurs when an average of any kind makes
diversity look like uniformity. When a group of items contains widely differing
values, any average will be a distorted representation of that group.

This fallacy shows up frequently, usually as a result of the blender
effect produced by the mean average. We Americans have an odd desire always
to know what the "average" is, perhaps because we have most regrettably
confused "average" with "normal." As a result we are offered and try to
adjust our lives by such dubious statistics as these:

The average woman is 30, married, and has 2.3 children.

The average American eats an average of 4.3 ounces of beef a day.

The average American husband commits adultery an average of 0.06 times
per year.

The average person weighs 150 pounds.

The average temperature in this desert area is 75 degrees. [It's 115 in
the summer and 35 in the winter--average it yourself!]

As these examples would indicate, often no kind of average can adequately
represent a group. Here, for instance, is a list of grades given in a class:

A
A
A
A
B
C
D
D
F
F
F
mean average is C
median average is C
mode average is A

Even if one of the averages is specified ("The median average is a C"),
does that information convey the true nature of the grades? We could avoid
the unspecified average fallacy here, but any statement of average will
commit the convergent average fallacy because this list cannot be accurately
characterized by an average.

Here are some other examples of averages that produce fallacious convergence:

The average man reads five comic strips a day; the average woman reads
two.

Nationwide mean average gasoline mileage for all cars is 15 mpg.

An average of twenty-two minutes is required for the average American to
eat the average meal.

False Compromise. Also called false mean and extremes, this fallacy
exploits the seemingly innate desire we all have for moderation. To accuse
someone of going too far or being at the extreme has long been a common
way of criticizing a perceived departure from acceptability. Stability,
security, and reasonableness are all associated with the middle--the mean
between the extremes of either side.

But the desire to steer a middle course can be exploited in argument
because the true mean and the nature and extent of the extremes are open
to question and debate. In fact, any position can be represented as the
mean between two extremes, so that what at first appears to be the middle
road, the compromise, the position of reason and moderation, may actually
be a fanatical view cleverly placed between two fabricated extremes. For
this reason alone, "compromise" and "middle" positions should not be accepted
blindly; but further, sometimes the best position is nearer one extreme
than the other and is not right in the middle.

Avoid the right wing fringe of the Republicans and the left wing fringe
of the socialists: join the Democratic party.

Avoid the rightist extreme of anarchy and the leftist extreme of big-government
Democrats: join the party of moderation, the Republicans.

Avoid the fanatic capitalism of the Democrats and Republicans, and avoid
the other extreme of those totalitarian communists--join the socialists,
the mean between extremes.

At one extreme are those who oppose all abortion services, and at the other
are those who want free, government paid abortions available to anyone.
I favor a middle, moderate position of allowing abortions when paid for
by the patient and approved by her doctor.

Exercise 1

For each discourse below, name the fallacy or fallacies committed. If the
discourse contains no fallacy, so state. Feel free to make brief comments
pertinent to uncertain or context-dependent cases.

1. One question I would like to ask my opponent: Why are you always
trying to hide your real position?

2. All serious students get straight A's. If you aren't getting straight
A's, then you are obviously not a serious student.

3. We have discovered a very high statistical correlation between exposure
to ultraviolet light at high intensities for prolonged periods and skin
cancer. And there is a strong correlation between not having skin cancer
and not being exposed to high levels of UV for long periods. I think these
findings show a good probability that long exposure to UV at high levels
will create a higher risk of skin cancer than with non exposure.

4. Describe what will happen if you take a laser beam that can burn
through anything and turn it on against a wall that cannot be penetrated
by anything.

5. It's as simple as this: either we build the Advanced Technology Bomber
right now and in quantity or we will always be a second rate military power,
in danger of invasion or attack. What's your choice?

6. This administration has been attacked for going too far on affirmative
action and it has been attacked for not going far enough. I think that
shows that we have taken the proper middle road.

7. I'll tell you one thing: if we legalized heroin and marijuana, then
organized crime couldn't make any money on it and would stop pushing it.
Its legality would also make it lose its appeal and soon there would be
no drug problem in the U.S.

8. There are no believable statements for modern man to live by. Now
we have only to choose which collection of myths we will adopt for our
"philosophy."

9. You can now save up to 75% on selected items at Frimpson's Department
Store.

1. Distinguish between a contrary to fact fallacy and an acceptable
conditional syllogism. What are the factors that permit you to judge?

Test Yourself

For each question, choose the single best answer.

1. But despite such public accolades, a sober, sometimes even bitter
argument rages within the profession itself. Specifically, it is whether
psychotherapy is a science or a superstition ennobled as a discipline.
Are the emotionally distressed the recipients of the fruits of a true psychological
revolution or the victims of a cheap psychic nostrum? --Martin L. Gross

2. Since I define "mental processes" as the conscious experiences of
which someone is aware, the concept of "unconscious mental processes" is,
in my opinion, an unacceptable contradiction in terms. --Arturo Rosenblueth

4. Unlike those intemperate people who get drunk every night, and still
unlike those sourpuss teetotalers who never drink at all, I favor the happy
medium of getting drunk on weekends. Everyone should agree with this middle
position, which favors neither extreme.